On the Zakai Equation of Filtering with Gaussian Noise

Abstract

The purpose of this work is to present an analogue of the Zakai type equation in case the noise is a Gaussian process, including fractional Brownian motion (fBm). The problem is of interest in view of the fact that the signal sent through the internet is contaminated by the noise given by fBm ([6]). Recently, a similar filtering problem with fBm noise was considered in [1]. However, the authors considered a non—Markovian signal process. The assumption of the Markov property on the signal is realistic. This also leads to a recursive equation, which is easily tractable, and is widely studied ([11, 5]).